1. Field of Invention
The present invention pertains to finite element analysis. In particular, the present invention pertains to smoothing finite element analysis generated tire footprints.
2. Description of Related Art
A commonly recognized problem associated with conventional finite element analysis (FEA) techniques is that processor resources (e.g. dynamic memory, processing cycles, non-volatile storage, etc.), as well as processing time required to perform an FEA analysis, increase in response to increases in the FEA mesh resolution. Processor resources increase because each point of intersection of an FEA mesh applied to a finite element model represents a point for which processing, storage, and analysis is performed. Depending upon the nature of the finite element analysis to be performed, processor resources may rise significantly in response to a slight increase in the applied FEA mesh resolution.
Unfortunately, the discrete nature of finite element analysis is most pronounced at the outer edges of the finite element analysis region. In FEA applications used to display visual output of results, the discrete nature of finite element analysis manifests itself as extended, truncated and/or rough edges in generated images. One conventional approach for improving the appearance of generated images is to increase the resolution of the FEA mesh. Unfortunately, FEA mesh resolutions sufficiently fine to smooth image boundaries typically result in unacceptable increases in processor resources, as described above.
Researchers attempting to use finite element analysis to study contact regions between objects in contact with one another are particularly hard-hit by the unfortunate relationship between FEA mesh resolutions and increases in processor resources, described above. This is because contact regions between objects are typically characterized by an outer boundary which defines the area of contact between the objects. An inability of conventional finite element analysis techniques to provide timely and accurate contact region boundary information significantly reduces the value of finite element analysis to researchers in this field of study.
Hence, a need remains for a method and apparatus for improving the accuracy and resolution of the shape, or boundary, of a contact region of a finite element model deformed against a contact surface which does not significantly increase the computer resources and/or processing time necessary to perform the simulation. The results generated using the approach should be consistent with contact region boundary results produced by observed physical experiments under similar load conditions. Preferably, the approach should be compatible with and be capable of being integrated with existing finite element analysis toolsets and data.